Question

The number of constant functions from a set containing m elements to a set containing n elements is:
1. mn
2. m
3. n
4. m+n​

Answer 1

The correct answer is option C.

Given: Set containing m elements to a set containing n elements.

To Find: The number of constant functions.

Solution:

• For every elements in set A there is a element in set B.
• So, the mapping of each element of set A is with each element of set B.
• That is each element in set A is mapped with n elements.

Hence, the correct option is C.

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Answer 2

Answer:

Option (3) is the correct answer.

Step-by-step explanation:

Concept:-

The number of the constant function is the number of elements present in the co-domain, i.e.,

Number of constant functions = Number of elements in co-domain

According to the question,

The function is defined from the set A to the set B.

Clearly, the set $A$ is the $domain$ of the function.

And the set $B$ is the $co-domain$ of the function.

It is given that the set A contains m elements and the set B contains the n elements.

1) mn

Since mn is the product of the elements present in the sets A and B.

Thus, mn is not the number of the constant function.

Option (1) is incorrect.

2) m

Since m is the number of the elements present in the set A, i.e., domain of the function.

Thus, m is not the number of the constant function.

Option (2) is incorrect.

3) n

Since n is the number of the elements present in the set B, i.e., co-domain of the function.

Thus, n is the required number of the constant function.

Option (3) is correct.

4) m + n

Since m + n is the sum of the elements present in the sets A and B.

Thus, m + n is not the number of the constant function.

Option (4) is incorrect.

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